The Nimbus of Pathos feature from the College of Tragedy bard states that after 1 minute the target immediately drops to 0 hit points and is dying. Does death ward prevent that?
The "drops to 0 hit points" in Nimbus of Pathos is not "as a result of damage".
Death ward states:
The first time the target would drop to 0 hit points as a result of taking damage
However, Nimbus of Pathos states:
When this effect ends, the creature immediately drops to 0 hit points and is dying.
This effect does not deal damage. Since you are dropping to 0 hit points without taking damage, death ward has no effect.
Rules, and stuff written by Matt Mercer, don't always mesh
I think the RAW is covered by the answer from Thomas Markov, but Matt's content is notoriously poorly written so RAW isn't the best method to answer this question, in my opinion.
Unfortunately that leaves it mostly up to the DM, but I think Death Ward, which is a 4th level spell intended to stop you from being killed, should be allowed to do its single job and stop you from being killed.
Therefore you would drop to 0hp, but Death Ward would then kick in and raise you to 1.
My additional logic for this is because frankly this class is absolutely terribly weak. Having a capstone that kills you defies all standard logic of the game, and it isn't really that powerful of a capstone anyway so it won't cause problems that you actually manage to survive it. If anything I am not sure it is even worth a 4th level slot.